Discount rates and greenhouse gas emissions

How much should we spend to curb greenhouse gas emissions?

A big part of this question concerns the discount rate: the rate used to balance future expected benefits against today's costs of reducing emissions. Common thinking among some economists is that since you can put money in the stock market and expect a decent return over the long run, benefits in the distant future should be worth a lot less in today's dollars. This thinking suggests we shouldn't spend much on reducing greenhouse gases emissions.

That first-cut thinking by economists gets the economics wrong.

Consider that we might also think of current emission reductions as insurance. We buy insurance all the time and insurance premiums typically have negative expected returns. We're willing to accept that negative expected return because insurance pays big indemnities in unusually bad circumstances when we really need the money.

Curbing greenhouse gas emissions seems a lot more like buying insurance than investing in stocks, and this pushes the discount rate down a lot.

Let's step back and spell out all the pieces.

There are three essential considerations in choosing the discount rate: (1) the benefits will accrue many years in the future; (2) the benefits, like climate change itself, are highly uncertain; (3) the discount rate itself is uncertain.

(1) means small differences in the discount rate have a huge effect on the bottom line because the discount rate interacts with time exponentially; (2) matters because risk premiums appear to be really high; (3) matters for the same reason (1) matters, as I'll explain below.

Standard theory says the discount rate (d) is the sum up of three parts:

d = eta + g + r

eta is the value of consuming something today verses consuming it tomorrow, holding all else the same. Stern set this parameter to 1% and some felt that number was too low, probably because they misinterpreted this number as the discount rate itself. I think 1% is reasonable. Those hugely worried about intergenerational equality might set eta equal to zero. In any case, its probably smallest and least important part of d.

g is economic growth, adjusted by the inverse elasticity of intertemporal substitution, if not 1 (log utility). Greater growth means lower marginal utility in the future and a higher discount rate. Given historical growth rates, log utility would put this number around 3%, higher if the elasticity of intertemporal substitution is low.

r is the risk premium. Because investments in reduced GHG emissions will pay off most in bad times, if climate change turns out to be a very bad thing rather than a mild or even beneficial thing, the risk premium is negative. This gets at the insurance/stock-market dichotomy above. Investments in assets like stocks, which pay off most in good times, have a positive risk premium. Given historical estimates of risk premiums, this could be a big negative number.

A reasonable person can probably justify anything in the range of -3 to + 5% for the sum of thee three numbers. That's a big range. And yes, it could be a negative number. How could it be negative? It's that negative risk premium, which could be huge. Subtract a big risk premium from a typical real bond rate and you're in negative territory.

Okay, now (3), what's the implication of the discount rate itself being uncertain?

Weitzman showed that this pushes the effective rate down. This follows from the simple fact that the present value of future benefits decline at a decreasing rate with the discount rate. In other words, the value function is convex. If it turns out that the discount rate is low or negative, expected returns are absolutely huge. So, we should err on the downside when we choose a
discount rate.

In sum, I have no idea how much we should spend reducing GHG emissions because I have no idea how costly reductions would be, the costs should warming occur, or how GHG affects all the possibilities. But I think a low discount rate, in the ballpark of zero, should be used when weighing current expenditures to future expected benefits. Moreover, I don't think a zero discount rate should be controversial among serious economists.

Nick Stern used low number but not as low as zero, and he got a lot of grief for it. I don't think grief was justified, except maybe he could have done a better job explaining why the number should be so low.

For more on this, read Martin Weitzman. John Quiggen has a nice writup on this too. I think I've summarized the essence of their arguments here.


  1. A discount rate is fiendishly difficult to calculate. France sets it at 5% for 50 years and then down to 3% after (or maybe 4% and 2%). USA government officials weren't sure if healthcare costs are being covered by cigarette taxes.

    eta should recognize an individual's lifetime consumption preference; shouldn't be a static 1% annual discount. People don't mind saving until retirement but prefer to consume while alive. Some/most of the estate should be redistributed but you have to integrate personal consumption patterns.
    g depends on whether calamities befall and whether opportunities are harnessed. I'm reading a boring history lesson of when civil order has historically broken down, the thesis being loss of skills and property crimes can prevent recovery. I'd guess 50 years without teaching globally would be enough to threaten regress to pre-IR.
    Apart from reduced probability of recovery, I've valued humanity at $1 quadrillion and tried to measure the risks and rewards against eachother to determine which have economic growth primacy.

    A whole bunch cost a few hundred billions annually. Cigarette health care costs. Alcohol deviance. 1/100 year AGW-ed flood costs for future cities is $35T, so $350B annually. WWIII $6.3T/yr, but retarded ability to recover is more important. A nuke winter regional war $1.3T/yr. Nosocomial infections $400B/yr. 50% lethal Avian Flu mutation $3.6T/yr. 3% lethal, $260B/yr.

    The list is endless and probability estimates are tough (nuke close calls are public but how to estimate Avian Flu mutation odds?). Better patent systems or human development might be a massive upside. Obesity could be China's AIDS. Famines are probably huge. I hoping to find some modular civil defense solutions. AGW will wipe out farm land that might approach the value of cities flooded.

    I view changing the economic growth rate as more useful for an economist than predicted it. Looking at predictions, it looks like you need to find factors that affect long term growth at least $trillions$ annually, to crowd out WWIII odds. AGW is probably there; the long-term increase in climate churn probably hurts recovery from catastrophic events; a blueprint to easily wean off coal or to safely cool down from a baked planet might be priceless.

    The risk premium of a strategic wheat reserve is insanely negative. But maybe will be even cheaper to store in future.

  2. A factor that will affect very long-term economic growth (50-500yrs??) is population growth. Here I see the key technology being in-situ propellant extraction (NASA knows this) from satellite/comet mines. I don't think Earth can house hundreds of billions.

  3. For time discounting I think it's pragmatic to consider investment over three time periods. I'll call them Republican, Democrat, and Utilitarian optimal. The idea being to lay out long-term options.

    By Republican I mean primarily self-interested. Here, I'll take the GDP of the world and translate it into demographics. The expected longevity of the world's median wealth will dominate this calculation. If most of the world's wealth is in the form of 60 year old men who will live another 26 years, this 26 years is the timescale over which to consider ROE. Not entirely; we don't want the world to end after 26 years. Still working out a discount rate heuristic post rich people deaths.

    Utiliatarian optimal is maximizing wealth for all humans who will and do live. Dominated by long-term uncertainty. I'd think the lifespan of the wealthiest actors again is primary (because our society is more predictable over this timescale), but this choice would put way more emphasis on future generations than the Republican growth rate.

    Finally Democrat. Not really sure what this is but it is meant to be a realistic goal for progressive peoples. Might just use the CDI's highest rated nations as a proxy and try to guess from their budgets what they are implictly using as a discount rate. Add the most progressive developing world (Bostwana?) nations's implicit discount rates too.

  4. Forbes's 793 billionaires are 63.7 years old in 2009 (71 in 2008). The USA 2004 actuary tables suggest a life expectancy of 18.11 years for a 63 year old.
    For now I'll use maximizing GDP over 18 years as the Republican investment discount rate. There is some merit to trickle down arguments so prolly no need to consider anything else. Probably you get high growth over 18 years and than trending towards slower or negative growth rates over the long-term.

  5. Phillip:

    Thanks for all your thoughtful comments. I wish I would get more of them!

    You raise a lot of interesting points. While they are all relevant to costs and benefits generally, I'm not sure if they all pertain to the discount rate.

    I'll touch on a couple issues here:

    eta might be adjusted to capture the life-cycle effects your mentioning, especially if (a) we think this is a big number for at least some groups of people, or (b) we think the age distribution of the popuation will change a lot. Maybe. But I still think this is small potatoes compared to the other factors.

    A second point you raise is that economic growth is uncertain. Boy that sure rings true at times like now. I guess I'm an optimist and believe will probably get back to that usual 3% growth. But if we think the trend growth will decline in the future, then that implies a lower discount rate. If we're uncertain about growth, well, I think I dealt with that.

    The big numbers are growth, risk, and uncertainty about what the overall rate should be. I still cannot see how an objective interpretation of these could be far from zero, in sum.

    That's why I say a near-zero rate should not be controversial. Despite the logic, I imagine many economists would feel very uncomfortable with a zero discount rate.

  6. GDP isn't the best measure for measuring g. For instance, AGW will make freshwater more expensive. Right now it is practically free in many developed cities. This will also affect r (I hadn't considered counter-cyclicality); a world with more expensive water is more risky. It may be the main reason (along with reliable food supply) Africa stagnates while China grows.
    If you really want to be banal about it, there should be another minor variable that combines RxG in the formula. Also, in the future we will almost certainly not be placing the primacy upon GDP we are now. So no sense using it now as the be all and end all.
    Off the top of my head, aggregate # of healthy years not spent working an unhappy job (thinking sweatshop mainly), is a good proxy. These sorts of indices are being drafted in the mainstream now. If you are really optmistic about tech progress affecting human quality-of-living for the good (maybe more of a dream for next century), it probably means ETAxG is another variable to consider. If we get healthy crack cocaine or some magic pan-Earth relationship matchmaker computer program, it will make eta very positive at some point decades ahead, along with increasing the g quality-of-living GDP surrogate, at the same time.
    This suggests non-linearities, asymptopes and exponential growth; I think the formula needs a calculus fix. I'll try to fix it. I'm just today thinking through the ramifications of r. If there is an eta*g, and a g*r, there is likely an eta*r and a eta*g*r. Question is whether any of these are significant enough over reasonable (for AGW 10000yrs to next ice age is an upper bound but I'm sure can be defined better) time-scales compared to the base 3 variables.

  7. I guess whther you define g as GDP growth or quality of living isn't too important. I assume the future holds happier and more people and it probably works out the same as assuming 3% GDP growth.
    The caveat my rambly earlier posts pointed out was whatever you are working on this problem for problem strongly affects the future growth rate itself, but this can be mathed out.

    I just has an idea for the ethics of eta. eta measures a ratio of present consumption to all other utilities of capital. Present consumption should be higher if other utilities are less efficient, and spending on other utilities (investment, consumption by 3rd world) should be higher if present consumption is less efficient (go all out on climate change spending if a nation of crackheads or luxury art auction addicts). Powerful.


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